The same construction works in the limit \(K=-1\) , that is, for locally convex pleated surfaces in \(\mathbb {ADS}^3\) . The corresponding map is then an earthquake, and earthquakes can in this manner be considered as limit cases of landslides, see [1]}, [2]}, and an earthquake map from \({\mathbb {H}}^2\)  to \({\mathbb {H}}^2\)  is associated to any locally convex complete pleated surface in \(\mathbb {ADS}^33\)  with bounded measured pleating lamination, see [3]}.
